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Thank you!

THX....!!!!

[ It does avoid that nasty integral...LOL !!!   ]

Density = Mass / Volume              cross multiply

Mass =Volume x Density

Mass = 4.50 x 19.3 =86.85 grams.

If the third side = 17....we have a right triangle

So...the greatest integer length of remaining side  is 16

And because of the triangle inequality

8 + unknown side > 15

unknown side > 7

So....the possible integer lengths are  [ 8 , 16 ]

sorry

The figure below is not drawn to scale. We are given that angle ADB is obtuse.
Which of the following statements must be true?

(i)  BD (ii) CD
Enter the letter of the multiple choice option below:

A: (i) only
B: (ii) only
C: (i) and (ii)

D: neither (i) nor (ii)

Ohh wow thank you, :D

Just what I was looking for, it makes a lot more sense now.

What are the statements ????

C. The points on the following shape represent the areas in which Chris will decorate his room with the ribbons. Find the area of the following shape. You must show all work to receive credit.

Figure ABCDEF is shown. A is located at 5, negative 8. B is located at 11, negative 8. C is located at 11, 0. D is located at 6, negative 3. E is located at 4, negative 3. F is located at 0, negative 6

We can use something known as "Pick's Theorem" to solve this

The area is given by

Boundary Lattice Points / 2  +  Interior Lattice Points -  1

[ A lattice point is a point that has integer coordinates ]...so we have

Boundary Lattice Points = 19

Interior Lattice Points = 43

So....the total area =    19/2 + 43 - 1   =   9.5 + 42   =  51.5 units^2

Just divide:  $13,561,623 million  / 309 million = $43,888.75 - Federal debt per capita in 2010.

If I understand your question:
This is the "closed form" of each term:
a_n = 1/2 (6 n + (-1)^(n + 1) + 13). 
And the number 235236(n) is a multiple of 7 in the following bases:
n = 10, 12, 16, 18, 22, 24, 28, 30, 34, 36, 40, 42, 46, 48, 52, 54, 58, 60, 64, 66, 70, 72, 76, 78, 82, 84, 88, 90, 94, 96, 100.

this is the picture to the problem sorry cphill

let me show it

B. Chris is now trying to buy ribbons to decorate his room. A point T on a segment with endpoints D(1, 4) and F(7, 1) partitions the segment in a 2:1 ratio. Find T. You must show all work to receive credit.

We can find this as follows

Note that T is 2/3 of the distance from A to D

T  =  [ 1 + (2/3)(7 - 1) , 4 + (2/3)(1 - 4) ]   =  [ 1 + (2/3)(6) , 4 + (2/3)(-3) ] = [ 1 + 4 , 4 - 2] =

(5, 2 )  = T

(A)

B = (-2, 4)

C  = (1, 1)    the slope between these is    [ 4 - 1 ] / [ -2 - 1 ] = 3 / - 3   = - 1

E = (4, 4)

F = (6, 2)     the slope etween these is  [ 4 - 2 ] / [4 - 6]  = 2 / - 2   =  -1

So....the slopes are the same

No figure is shown....

Thank you.

Here's another way to do this with similar triangles....it is much easier

First....calculate DE as I did before = 6.5

Note that angle BXC = angle DXE  (vertical angles)

Angle DEX = Angle CBX   (alternate interior angles between  parallels )

So  triangle BXC is isimilar to triangle EXD

Since base ED is 1/2 of BC

Then the height of triangle EXD is 1/2 that of triangle BXC

So y = 4.5 is split into  tree equal parts....and the height of BXC is (2/3)of these = 3 

Then  area of triangle EXD = 1/4 area of triangle BXC

Area of BXC = (1/2)(3)(13) =  39/2  = 19.5

And the area of EXD = (39/8)

And the area of triangle ADE is (1/2)(4.5)(6.5) = (117/8)

So the area of AEXD = area of triangle EXD + area of triangle of triangle ADE =

(39/8 + 117/8) = (156/8) = 19.5

So the ratios of BXC / AEXD = 19.5 /19.5  =  1

Write it properly and you might have a better chance of a timely answer.

Just edit it and take the $ signs away.

You can either evaluate it in base 7(if you have a calculator or a computer program that can do that) or convert the individual integers from base 7 to 10 and then evaluate.

ln ((5304552^3 + 2112)^2 - 3230004) / sqrt(1621) = 3.066365143.....{This is the answer in base 7.}

Converting the individual integers from base 7 to base 10, the entire expression looks like this:
ln((640320^3 + 744)^2 - 393768) / sqrt(652) =3.14159265358..........etc., which is, surprise, surprise, good old Pi.
 

Thanks much!!!

Thank you very much! I agree, figuring out the range was a little more difficult for me to understand. Good explanation!

The scale factor is 1.4

The increase in volume is the cube of this = (1.4)^3 = 2.744  times

So....the percentage increase is  [2.744 - 1 ] x 100% =  174.4%

How many Sig Figs are in  \( 3.4\times {10}^{4}\)

Significant firgues with scientific notation is very easy.  There are 2 digits in 3.4 so there are 2 significant figures.

Only the significant part should be written in sci fi although if there is more to the question (like you have worked out the number yourself) you may need to be careful.

3.40000 * 10^4     has 6 significant figures   

Thanks EP I had forgotten that :)